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Two remarks on elementary theories of groups obtained by free constructions

Mathematical Logic Quarterly 59 (1-2):12-18 (2013)

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On the generic type of the free group.Rizos Sklinos - 2011 - Journal of Symbolic Logic 76 (1):227 - 234.details We answer a question raised in [9], that is whether the infinite weight of the generic type of the free group is witnessed in F ω . We also prove that the set of primitive elements in finite rank free groups is not uniformly definable. As a corollary, we observe that the generic type over the empty set is not isolated. Finally, we show that uncountable free groups are not N₁-homogeneous. Logic and Philosophy of Logic Model Theory in Logic and Philosophy of Logic Direct download (7 more) Export citation Bookmark 5 citations
Groupes Stables, avec types génériques réguliers.Bruno Poizat - 1983 - Journal of Symbolic Logic 48 (2):339-355.details Logic and Philosophy of Logic Model Theory in Logic and Philosophy of Logic Direct download (8 more) Export citation Bookmark 9 citations
Generix Never Gives Up.Eric Jaligot - 2006 - Journal of Symbolic Logic 71 (2):599 - 610.details We prove conjugacy and generic disjointness of generous Carter subgroups in groups of finite Morley rank. We elaborate on groups with a generous Carter subgroup and on a minimal counterexample to the Genericity Conjecture. Logic and Philosophy of Logic Model Theory in Logic and Philosophy of Logic Direct download (6 more) Export citation Bookmark 5 citations

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